Part One: MATH 11Substitution 13 Defined Functions 23 Math Notes 26 Number Theory 30 Geometry 46 Coordinate Geometry 153 Elimination Strategies 175 Inequalities 185 Fractions & Decimals 193 Equations 202 Averages 213 Ratio & Proportion 221 Exponents & Roots 234 Factoring 246 Algebraic Expressions 251 Percents 258 Graphs 270 Word Problems 299 Sequences & Series 315 Counting 322 Probability & Statistics 329 Permutations & Combinations 342 Functions 383 Miscellaneous Problems 403
Part Two: DATA SUFFICIENCY 415
Part Three: SUMMARY OF MATH PROPERTIES 507
Part Four: DIAGNOSTIC/REVIEW TEST 517
Although the GMAT is a difficult test, it is a very learnable test. This is not to say that the GMAT is "beatable." There is no bag of tricks that will show you how to master it overnight. You probably have already realized this. Some books, nevertheless, offer "inside stuff" or "tricks" which they claim will enable you to beat the test. These include declaring that answer-choices B, C, or D are more likely to be correct than choices A or E. This tactic, like most of its type, does not work. It is offered to give the student the feeling that he or she is getting the scoop on the test.
The GMAT cannot be "beaten." But it can be masteredthrough hard work, analytical thought, and by training yourself to think like a test writer. Many of the exercises in this book are designed to prompt you to think like a test writer. For example, you will find "Duals." These are pairs of similar problems in which only one property is different. They illustrate the process of creating GMAT questions.
The GMAT math section is not easynor is this book. To improve your GMAT math score, you must be willing to work; if you study hard and master the techniques in this book, your score will improvesignificantly.
This book will introduce you to numerous analytic techniques that will help you immensely, not only on the GMAT but in business school as well. For this reason, studying for the GMAT can be a rewarding and satisfying experience.
To insure that you perform at your expected level on the actual GMAT, you need to develop a level of mathematical skill that is greater than what is tested on the GMAT. Hence, about 10% of the math problems in this book (labeled "Very Hard") are harder than actual GMAT math problems.
Although the quick-fix method is not offered in this book, about 15% of the material is dedicated to studying how the questions are constructed. Knowing how the problems are written and how the test writers think will give you useful insight into the problems and make them less mysterious. Moreover, familiarity with the GMAT's structure will help reduce your anxiety. The more you know about this test, the less anxious you will be the day you take it.